Recent developments concerning generic spacelike singularities

Abstract

This is a review of recent progress concerning generic spacelike singularities in general relativity. For brevity the main focus is on singularities in vacuum spacetimes, although the connection with, and the role of, matter for generic singularity formation is also commented on. The paper describes recent developments in two areas and show how these are connected within the context of the conformally Hubble-normalized state space approach. The first area is oscillatory singularities in spatially homogeneous cosmology and the connection between asymptotic behaviour and heteroclinic chains. The second area concerns oscillatory singularities in inhomogeneous models, especially spike chains and recurring spikes. The review also outlines some underlying reasons for why the structures that are the foundation for generic oscillatory behaviour exists at all, which entails discussing how underlying physical principles and applications of solution generating techniques yield hierarchical structures and connections between them. Finally, it is pointed out that recent progress concerning generic singularities motivates some speculations that suggest that a paradigm shift concerning their physical role, and what mathematical issues to address, might be in order.

32 pages; plenary contribution to ERE2012

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• Understanding Gravitational Entropy of Black Holes: A New Proposal via Curvature Invariants
• Open problems in mathematical physics
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• Mixmaster dynamics in the dust time gauge
• Chaos in spatially homogeneous Hořava-Lifshitz subcritical cosmologies
• Onset of synchronization in coupled Mixmaster oscillators
• Periodic orbits in Hořava-Lifshitz cosmologies